Surface tension as the destabiliser of a vortical interface

Abstract

We study the dynamics of an initially flat interface between two immiscible fluids, with a vortex situated on it. We show how surface tension causes vorticity generation at a general curved interface. This creates a velocity jump across the interface which increases quadratically in time, and causes the Kelvin-Helmholtz instability. Surface tension thus acts as a destabiliser by vorticity creation, winning over its own tendency to stabilize by smoothing out interfacial perturbations to reduce surface energy. We further show that this instability is manifested within the vortex core at times larger than $\sim (k We)^{1/4}$ for a Weber number $We$ and perturbation wavenumber $k$, destroying the flow structure. The vorticity peels off into small-scale structures away from the interface. Using energy balance we provide the growth with time in total interface length. A density difference between the fluids produces additional instabilities outside the vortex core due to centrifugal effects. We demonstrate the importance of this mechanism in two-dimensional turbulence simulations with a prescribed initial interface. We show an increase in kinetic energy at large wave numbers due to the creation of small-scale vortices by the action of surface tension.